• Corpus ID: 184488209

Abelian tropical covers

@article{Len2019AbelianTC,
  title={Abelian tropical covers},
  author={Yoav Len and Martin Ulirsch and Dmitry Zakharov},
  journal={arXiv: Algebraic Geometry},
  year={2019}
}
The goal of this article is to classify unramified covers of a fixed tropical base curve $\Gamma$ with an action of a finite abelian group G that preserves and acts transitively on the fibers of the cover. We introduce the notion of dilated cohomology groups for a tropical curve $\Gamma$, which generalize simplicial cohomology groups of $\Gamma$ with coefficients in G by allowing nontrivial stabilizers at vertices and edges. We show that G-covers of $\Gamma$ with a given collection of… 

Figures from this paper

Prym–Brill–Noether Loci of Special Curves
We use Young tableaux to compute the dimension of $V^r$, the Prym-Brill-Noether locus of a folded chain of loops of any gonality. This tropical result yields a new upper bound on the dimensions of
Tropical Curves and Covers and Their Moduli Spaces
Tropical geometry can be viewed as an efficient combinatorial tool to study degenerations in algebraic geometry. Abstract tropical curves are essentially metric graphs, and covers of tropical curves
Kirchhoff’s theorem for Prym varieties
Abstract We prove an analogue of Kirchhoff’s matrix tree theorem for computing the volume of the tropical Prym variety for double covers of metric graphs. We interpret the formula in terms of a
Tropical double ramification loci
Motivated by the realizability problem for principal tropical divisors with a fixed ramification profile, we explore the tropical geometry of the double ramification locus in

References

SHOWING 1-10 OF 45 REFERENCES
Tropical hyperelliptic curves
We study the locus of tropical hyperelliptic curves inside the moduli space of tropical curves of genus g. We define a harmonic morphism of metric graphs and prove that a metric graph is
Genus Bounds for Harmonic Group Actions on Finite Graphs
This paper develops graph analogues of the genus bounds for the maximal size of an automorphism group of a compact Riemann surface of genus $g\ge 2$. Inspired by the work of M. Baker and S. Norine on
Tropicalization of theta characteristics, double covers, and Prym varieties
We study the behavior of theta characteristics on an algebraic curve under the specialization map to a tropical curve. We show that each effective theta characteristic on the tropical curve is the
Skeletons of Prym varieties and Brill–Noether theory
We show that the non-Archimedean skeleton of the Prym variety associated to an unramified double cover of an algebraic curve is naturally isomorphic (as a principally polarized tropical abelian
Tropicalization is a non-Archimedean analytic stack quotient
For a complex toric variety $X$ the logarithmic absolute value induces a natural retraction of $X$ onto the set of its non-negative points and this retraction can be identified with a quotient of
Lifting harmonic morphisms II: tropical curves and metrized complexes
In this paper we prove several lifting theorems for morphisms of tropical curves. We interpret the obstruction to lifting a finite harmonic morphism of augmented metric graphs to a morphism of
Tropicalizing the space of admissible covers
We study the relationship between tropical and classical Hurwitz moduli spaces. Following recent work of Abramovich, Caporaso and Payne, we outline a tropicalization for the moduli space of
A MODULI STACK OF TROPICAL CURVES
We contribute to the foundations of tropical geometry with a view toward formulating tropical moduli problems, and with the moduli space of curves as our main example. We propose a moduli functor for
...
...